In this section, a perfect gas model is presented: all the particles are independent, without any interaction.

Remark:

A perfect gas corresponds to the case where the kinetic energy of the particles is large with respect to the typical interaction energy. Nevertheless, collisions between particles that can be neglected are necessary for the thermodynamical equilibrium to establish.

Classical approximation (see section secdistclassi) allows to replace the sum over the quantum states by an integral of the exponential of the classical hamiltonian H(qi,pi){\displaystyle H(q_{i},p_{i})}. The price to pay is just to take into account a proportionality factor 12πℏ{\displaystyle {\frac {1}{2\pi \hbar }}}. Partition function z{\displaystyle z} associated to one particle is: